This invention relates to analytical methods of optimizing conditions for powder forging and, more particularly, to methods of optimizing the design of a die, operational conditions for the forging process such as pressure and flow rate and/or conditions on the materials such as the mixing ratio of the liquid, binder and powder material, as well as the particle size distribution.
When an extrusion forging process using a metallic powder material is analyzed by a finite element method, only shearing work (defined as the product of shearing strain and distance moved) is required to be considered, and there is no need to consider the bulk work (defined as the product of the bulk pressure due to a volume change and distance) because metallic powder materials consist of perfect arrays of electrons and their atomic configurations do not collapse even if pressure is applied. However, there have hardly been any attempts to carry out a three-dimensional finite element analysis for the forging process for a bulk metal.
In the case of powders of ceramic materials, by contrast as schematically shown in FIG. 4, particles 1 touch one another directly in some parts, while they touch one another through a liquid 2 or a gas phase 3 in some other parts. Although its overall shape will change when an external force is applied, there will be no such overall deformation in the absence of any external force. In a finite element analysis of powder forging such as forging by extrusion of such a material, therefore, the ratio of bulk work to internal work (defines as the sum of shearing work and bulk work) is not negligible. In other words, a plastic flow cannot be analyzed with high accuracy by computer simulation with a software program designed for finite element analysis for the case of a metallic material.
FIGS. 5 and 6, in which only the upper half of a die 4 is shown cross-sectionally, illustrate the finite element method of analysis by conventional Lagrangian description. If the interior of the die 4 is filled with a material in the condition illustrated in FIG. 4 (only five elements 6 for a finite element method of analysis being shown in FIG. 5 for convenience), and if this material is pushed from one side by a pressure-applying member 5, there may arise gaps 7 between the undeformable inner wall of the die 4 and the elements 6 and/or penetrations 8 of the die wall by an element 6 used in the finite element method of analysis as shown in FIG. 6. Consequently, the conservation of volume may fail to hold according to a conventional method of analysis. In other words, errors are introduced, and accurate calculations are impossible. Thus, three-dimensional dies could not be analyzed by a prior art method, and there has not been developed a system incorporating the arbitrary Lagrangian-Eulerian (ALE) method which is adapted to situations where contacts may exist between a powder material and a non-deformable tool.